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The history of the development of CUDA technology and its fundamental limitations are discribed. The article is intended for those readers who are not familiar with graphics adapter programming features but want to evaluate the possibilities for GPU computing applications.

The paper provides the mathematical and numerical models of the interrelated thermo- and hydrodynamic processes in the operational mode of development the unified oil-producing complex during the hydrogel flooding of the non-uniform oil reservoir exploited with a system of arbitrarily located injecting wells and producing wells equipped with submersible multistage electrical centrifugal pumps. A special feature of our approach is the modeling of the special ground-based equipment operation (control stations of submersible pumps, drossel devices on the head of producing wells), designed to regulate the operation modes of both the whole complex and its individual elements.

The complete differential model includes equations governing non-stationary two-phase five-component filtration in the reservoir, quasi-stationary heat and mass transfer in the wells and working channels of pumps. Special non-linear boundary conditions and dependencies simulate, respectively, the influence of the drossel diameter on the flow rate and pressure at the wellhead of each producing well and the frequency electric current on the performance characteristics of the submersible pump unit. Oil field development is also regulated by the change in bottom-hole pressure of each injection well, concentration of the gel-forming components pumping into the reservoir, their total volume and duration of injection. The problem is solved numerically using conservative difference schemes constructed on the base of the finite difference method, and developed iterative algorithms oriented on the parallel computing technologies. Numerical model is implemented in a software package which can be considered as the «Intellectual System of Wells» for the virtual control the oil field development.

The article presented the computational algorithm developed to study chemical processes in the internal flows of a multicomponent gas under the influence of laser radiation. The mathematical model is the gas dynamics’ equations with chemical reactions at low Mach numbers. It takes into account dissipative terms that describe the dynamics of a viscous heat-conducting medium with diffusion, chemical reactions and energy supply by laser radiation. This mathematical model is characterized by the presence of several very different time and spatial scales. The computational algorithm is based on a splitting scheme by physical processes. Each time integration step is divided into the following blocks: solving the equations of chemical kinetics, solving the equation for the radiation intensity, solving the convection-diffusion equations, calculating the dynamic component of pressure and calculating the correction of the velocity vector. The solution of a stiff system of chemical kinetics equations is carried out using a specialized explicit second-order accuracy scheme or a plug-in RADAU5 module. Numerical Rusanov flows and a WENO scheme of an increased order of approximation are used to find convective terms in the equations. The code based on the obtained algorithm has been developed using MPI parallel computing technology. The developed code is used to calculate the pyrolysis of ethane with radical reactions. The superequilibrium concentrations’ formation of radicals in the reactor volume is studied in detail. Numerical simulation of the reaction gas flow in a flat tube with laser radiation supply is carried out, which is in demand for the interpretation of experimental results. It is shown that laser radiation significantly increases the conversion of ethane and yields of target products at short lengths closer to the entrance to the reaction zone. Reducing the effective length of the reaction zone allows us to offer new solutions in the design of ethane conversion reactors into valuable hydrocarbons. The developed algorithm and program will find their application in the creation of new technologies of laser thermochemistry.

The aim of research is to develop software system for solving gas dynamic problem in multiply connected integration domains of regular shape by high-performance computing system. Comparison of the various technologies of parallel computing has been done. The program complex is implemented using multithreaded parallel systems to organize both multi-core and massively parallel calculation. The comparison of numerical results with known model problems solutions has been done. Research of performance of different computing platforms has been done.

The currently performed mathematical and computer modeling of thermal processes in technical systems is based on an assumption that all the parameters determining thermal processes are fully and unambiguously known and identified (i.e., determined). Meanwhile, experience has shown that parameters determining the thermal processes are of undefined interval-stochastic character, which in turn is responsible for the intervalstochastic nature of thermal processes in the electronic system. This means that the actual temperature values of each element in an technical system will be randomly distributed within their variation intervals. Therefore, the determinative approach to modeling of thermal processes that yields specific values of element temperatures does not allow one to adequately calculate temperature distribution in electronic systems. The interval-stochastic nature of the parameters determining the thermal processes depends on three groups of factors: (a) statistical technological variation of parameters of the elements when manufacturing and assembling the system; (b) the random nature of the factors caused by functioning of an technical system (fluctuations in current and voltage; power, temperatures, and flow rates of the cooling fluid and the medium inside the system); and (c) the randomness of ambient parameters (temperature, pressure, and flow rate). The interval-stochastic indeterminacy of the determinative factors in technical systems is irremediable; neglecting it causes errors when designing electronic systems. A method that allows modeling of unsteady interval-stochastic thermal processes in technical systems (including those upon interval indeterminacy of the determinative parameters) is developed in this paper. The method is based on obtaining and further solving equations for the unsteady statistical measures (mathematical expectations, variances and covariances) of the temperature distribution in an technical system at given variation intervals and the statistical measures of the determinative parameters. Application of the elaborated method to modeling of the interval-stochastic thermal process in a particular electronic system is considered.

We present results of a study aimed at identification of a controlled object’s channels based on postprocessing of measurements with development of a model of a multiple-input controlled object and subsequent active modelling experiment. The controlled object model is developed using approximation of its behavior by a neural network model using trends obtained during a passive experiment in the mode of normal operation. Recurrent neural network containing feedback elements allows to simulate behavior of dynamic objects; input and feedback time delays allow to simulate behavior of inertial objects with pure delay. The model was taught using examples of the object’s operation with a control system and is presented by a dynamic neural network and a model of a regulator with a known regulation function. The neural network model simulates the system’s behavior and is used to conduct active computing experiments. Neural network model allows to obtain the controlled object’s response to an exploratory stimulus, including a periodic one. The obtained complex frequency response is used to evaluate parameters of the object’s transfer system using the least squares method. We present an example of identification of a channel of the simulated control system. The simulated object has two input ports and one output port and varying transport delays in transfer channels. One of the input ports serves as a controlling stimulus, the second is a controlled perturbation. The controlled output value changes as a result of control stimulus produced by the regulator operating according to the proportional-integral regulation law based on deviation of the controlled value from the task. The obtained parameters of the object’s channels’ transfer functions are close to the parameters of the input simulated object. The obtained normalized error of the reaction for a single step-wise stimulus of the control system model developed based on identification of the simulated control system doesn’t exceed 0.08. The considered objects pertain to the class of technological processes with continuous production. Such objects are characteristic of chemical, metallurgic, mine-mill, pulp and paper, and other industries.

The paper presents the results of numerical simulation and experimental data on the high-speed penetration of the impactor into the obstacle. In the calculations, a discrete-element model has been used, based on the representation of the impactor and the target by a set of close packed interconnected particles. This class of models finds an increasingly wide application in the problems of high-speed interaction of bodies. In the previous works of the authors, the questions of application of the discrete-element model to the problem of the penetration of spherical impactors into massive targets were considered. On the basis of a comparative analysis of the data of computational and physical experiments, it was found out that for a wide class of high-speed penetration problems, a high accuracy of discrete-element modeling can be achieved using the two-parameter Lennard–Jones potential. The binding energy was identified as a function of the dynamic hardness of materials. It was shown that the use of this approach makes it possible to describe accurately the penetration process in the range of impactor velocities 500–2500 m/c.

In this paper, we compare the results of discrete-element modeling with experimental data on penetration of high-strength targets of different thickness by steel impactors. The use of computational parallelization technologies on graphic processors in combination with 3D visualization and animation of the results makes it possible to obtain detailed spatio-temporal patterns of the penetration process and compare them with experimental data.

A comparative analysis of the experimental and calculated data has shown a sufficiently high accuracy of discrete-element modeling for a wide range of target thicknesses: for thin targets pierced with preservation of the integrity of the deformed impactor, for targets of medium thickness, pierced with practically complete fragmentation of the impactor at the exit from the target, and for thick impenetrable targets.

The purpose of this work is to develop a universal computer program (solver) which solves kinetic Boltzmann equation for simulations of rarefied gas flows in complexly shaped devices. The structure of the solver is described in details. Its efficiency is demonstrated on an example of calculations of a modern many tubes Knudsen pump. The kinetic Boltzmann equation is solved by finite-difference method on discrete grid in spatial and velocity spaces. The differential advection operator is approximated by finite difference method. The calculation of the collision integral is based on the conservative projection method.

In the developed computational program the unstructured spatial mesh is generated using GMSH and may include prisms, tetrahedrons, hexahedrons and pyramids. The mesh is denser in areas of flow with large gradients of gas parameters. A three-dimensional velocity grid consists of cubic cells of equal volume.

A huge amount of calculations requires effective parallelization of the algorithm which is implemented in the program with the use of Message Passing Interface (MPI) technology. An information transfer from one node to another is implemented as a kind of boundary condition. As a result, every MPI node contains the information about only its part of the grid.

The main result of the work is presented in the graph of pressure difference in 2 reservoirs connected by a multitube Knudsen pump from Knudsen number. This characteristic of the Knudsen pump obtained by numerical methods shows the quality of the pump. Distributions of pressure, temperature and gas concentration in a steady state inside the pump and the reservoirs are presented as well.

The correctness of the solver is checked using two special test solutions of more simple boundary problems — test with temperature distribution between 2 planes with different temperatures and test with conservation of total gas mass.

The correctness of the obtained data for multitube Knudsen pump is checked using denser spatial and velocity grids, using more collisions in collision integral per time step.

We present a physico-mathematical statement of coupled geometrical and gas dynamics problem of intrachamber processes simulation and calculation of main internal ballistics characteristics of solid rocket motors in axisymmetric approximation. Method and numerical algorithm of solving the problem are described in this paper. We track the propellant burning surface using the level set method. This method allows us to implicitly represent the surface on a fixed Cartesian grid as zero-level of some function. Two-dimensional gas-dynamics equations describe a flow of combustion products in a solid rocket motor. Due to inconsistency of domain boundaries and nodes of computational grid, presence of ghost points lying outside the computational domain is taken into account. For setting the values of flow parameters in ghost points, we use the inverse Lax – Wendroff procedure. We discretize spatial derivatives of level set and gas-dynamics equations with standard WENO schemes of fifth and third-order respectively and time derivatives using total variation diminishing Runge –Kutta methods. We parallelize the presented numerical algorithm using CUDA technology and further optimize it with regard to peculiarities of graphics processors architecture.

Created software package is used for calculating internal ballistics characteristics of nozzleless solid rocket motor during main firing phase. On the base of obtained numerical results, we discuss efficiency of parallelization using CUDA technology and applying considered optimizations. It has been shown that implemented parallelization technique leads to a significant acceleration in comparison with central processes. Distributions of key parameters of combustion products flow in different periods of time have been presented in this paper. We make a comparison of obtained results between quasione-dimensional approach and developed numerical technique.

The article is devoted to modeling the shallow water hydrodynamic processes using the example of the Azov Sea. The article presents a mathematical model of the hydrodynamics of a shallow water body, which allows one to calculate three-dimensional fields of the velocity vector of movement of the aquatic environment. Application of regularizers according to B.N.Chetverushkin in the continuity equation led to a change in the method of calculating the pressure field, based on solving the wave equation. A discrete finite-difference scheme has been constructed for calculating pressure in an area whose linear vertical dimensions are significantly smaller than those in horizontal coordinate directions, which is typical for the geometry of shallow water bodies. The method and algorithm for solving grid equations with a tridiagonal preconditioner are described. The proposed method is used to solve grid equations that arise when calculating pressure for the three-dimensional problem of hydrodynamics of the Azov Sea. It is shown that the proposed method converges faster than the modified alternating triangular method. A parallel implementation of the proposed method for solving grid equations is presented and theoretical and practical estimates of the acceleration of the algorithm are carried out taking into account the latency time of the computing system. The results of computational experiments for solving problems of hydrodynamics of the Sea of Azov using the hybrid MPI + OpenMP technology are presented. The developed models and algorithms were used to reconstruct the environmental disaster that occurred in the Sea of Azov in 2001 and to solve the problem of the movement of the aquatic environment in estuary areas. Numerical experiments were carried out on the K-60 hybrid computing cluster of the Keldysh Institute of Applied Mathematics of Russian Academy of Sciences.